Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 564 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 16 (d) 15
2. 2.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
3. 3.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 20 (d) 21
5. 5.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 198 (d) 66
6. 6.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 144 (d) 154
7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 5 (d) 3
8. 8.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 30 (c) 33 (d) 90
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 17 (d) 7
10. 10.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 416 (d) 516
11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
12. 12.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 126 (d) 134
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 5 (d) 15
14. 14.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 144 (d) 48
15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 2 (b) 5 (c) 3 (d) 4
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 5 (d) 2
18. 18.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 52? (a) 6 (b) 3 (c) 4 (d) 5
20. 20.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 338 (b) 400 (c) 399 (d) 390
21. 21.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 6 (c) 3 (d) 5
22. 22.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 73 (c) 74 (d) 82
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 5 (b) 17 (c) 16 (d) 15
24. 24.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 597 (c) 607 (d) 476
25. 25.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 558 (c) 567 (d) 450
26. 26.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 27 (c) 9 (d) 81
27. 27.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 23 (b) 72 (c) 207 (d) 69
28. 28.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 142 (d) 132
29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 4 (d) 6
30. 30.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 421 (c) 420 (d) 352
31. 31.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 583 (c) 460 (d) 582
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 5 (b) 14 (c) 15 (d) 16
33. 33.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 6 (c) 21 (d) 54
34. 34.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 232 (c) 231 (d) 222
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 4 (d) 3
36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
38. 38.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 612 (d) 480
39. 39.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 42 (c) 33 (d) 34
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 7 (c) 17 (d) 18

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